Yes you should be able to see two screens. side by side. Normally the left screen (Primary) is bigger and would represent your main laptop flat panal screen. To the right of this would be a secondary smaller screen which would represent the tv output. If you cannot see this then it looks like you will need to change some advanced display settings or download the correct graphics card driver. The problem here is that the advanced settings for different manufacturers is generally different. I have had expreience with ATI and Nvidia settings and these are fairly easy to change.
I have to admit that I have never used tv out from an IBM thinkpad, my only experience is with Dell laptops, so I am assuming they work in the same way. Does the manual that came with your laptop not shed any light on the matter.